The concept of a generalized constraint - a bridge from natural languages to mathematics

The concept of a generalized constraint was introduced close to two decades ago. For a number of years, it lay dormant and unused. But then, in the mid-nineties, it found an important application as a basis for the methodology of computing with words (CW). The basis for the expectation is that as we move further into the age of machine intelligence and mechanized reasoning, the problem of natural language understanding looms larger and larger in importance and visibility. To deal with this problem what is needed is fuzzy logic - a logic in which everything is, or is allowed to be, a matter of degree. In this paper, the author discussed the concept of generalized constraint. With the concept of a generalized constraint as its centerpiece, PNL opens the door to a wide-ranging enlargement of the role of natural language in scientific theories, particularly there theories on what is human perceptions, judgment and small emotions play important roles.